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# More Multiplication Properties Exponents

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### More Multiplication Properties Exponents

1. 1. More Multiplication Properties of Exponents 06/01/09 PH 8-7 Bitsy Griffin
2. 2. Raising Powers to Powers <ul><li>For any nonzero number a and any integers m and n, </li></ul><ul><li>(a m ) n =a mn </li></ul><ul><li>(5 4 ) 2 =5 8 </li></ul>06/01/09 PH 8-7 Bitsy Griffin
3. 3. Raising Powers to Powers <ul><li>(2 3 ) 2 </li></ul><ul><li>(h 2 ) 4 </li></ul><ul><li>(3 3 ) 4 </li></ul><ul><li>(x 3 ) 6 </li></ul><ul><li>c 5 (c 3 ) 2 </li></ul>06/01/09 PH 8-7 Bitsy Griffin
4. 4. Raising Products to Powers <ul><li>For any nonzero number a and b and any integer n, </li></ul><ul><li>(ab) n =a n b n </li></ul><ul><li>(5y) 3 =5 3 y 3 </li></ul><ul><li>125y 3 </li></ul>06/01/09 PH 8-7 Bitsy Griffin
5. 5. Raising Products to Powers <ul><li>(3x) 4 =3 4 x 4 =?? </li></ul><ul><li>81x 4 </li></ul><ul><li>(7c) 2 =?? </li></ul><ul><li>49c 2 </li></ul><ul><li>(15z) 3 =?? </li></ul><ul><li>3375z 3 </li></ul>06/01/09 PH 8-7 Bitsy Griffin
6. 6. Raising Products to Powers <ul><li>(2x 2 ) 4 =?? </li></ul><ul><li>2 4 (x 2 ) 4 =?? </li></ul><ul><li>16x 8 </li></ul><ul><li>(4g 5 ) 2 =?? </li></ul><ul><li>4 2 (g 5 ) 2 =?? </li></ul><ul><li>16g 10 </li></ul>06/01/09 PH 8-7 Bitsy Griffin
7. 7. Raising Products to Powers <ul><li>(x -2 ) 2 (3xy 2 ) 4 =?? </li></ul><ul><li>x -4 3 4 x 4 (y 2 ) 4 =?? </li></ul><ul><li>3 4 x -4 x 4 y 8 =?? </li></ul><ul><li>81 x 0 y 8 =?? </li></ul><ul><li>81y 8 </li></ul>06/01/09 PH 8-7 Bitsy Griffin
8. 8. Raising Products to Powers <ul><li>(6mn) 3 (5m -3 ) 4 =?? </li></ul><ul><li>6 3 m 3 n 3 5 4 (m -3 ) 4 =?? </li></ul><ul><li>6 3 ● 5 4 m 3 m -12 n 3 =?? </li></ul><ul><li>6 3 ● 5 4 m 3 -12 n 3 =?? </li></ul><ul><li>(135,000 n 3 )/ m 9 </li></ul>06/01/09 PH 8-7 Bitsy Griffin
9. 9. Raising Products to Powers <ul><li>All objects, even resting ones, contain energy. The expression 10 -3 (3x10 8 ) 2 describes the amount of resting energy a raisin contains, where 10 -3 kg is the mass of the raisin. Simplify the expression. </li></ul>06/01/09 PH 8-7 Bitsy Griffin
10. 10. Real World Examples <ul><li>Use your calculator to help you. </li></ul><ul><li>Remember that you may have to convert from standard to scientific notation. </li></ul><ul><li>10 -3 (3x10 8 ) 2 </li></ul><ul><li>9x10 13 </li></ul>06/01/09 PH 8-7 Bitsy Griffin